what is the inverse of the function $f(x) = 49x^2$ when $x \ge 0$?

a. $f^{-1}(x) = 7\sqrt{x}$
b. $f^{-1}(x) = \frac{1}{7x}$
c. $f^{-1}(x) = 7x$
d. $f^{-1}(x) = \frac{\sqrt{x}}{7}$

Question

what is the inverse of the function $f(x) = 49x^2$ when $x \ge 0$?

a. $f^{-1}(x) = 7\sqrt{x}$
b. $f^{-1}(x) = \frac{1}{7x}$
c. $f^{-1}(x) = 7x$
d. $f^{-1}(x) = \frac{\sqrt{x}}{7}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Functions", "Finding Inverse Functions" ], "new_concepts": [], "current_concepts": [ "Inverse Functions", "Finding Inverse Functions" ] } ## Swap variables to find the inverse relation $$ \begin{aligned} y &= 49x^2, \quad x \ge 0 \ x &= 49y^2, \quad y \ge 0 \end{aligned} $$ ## Solve for y $$ \begin{aligned} y^2 &= \frac{x}{49} \ y &= \sqrt{\frac{x}{49}} \ y &= \frac{\sqrt{x}}{7} \end{aligned} $$ ## Write in inverse function notation $$ f^{-1}(x) = \frac{\sqrt{x}}{7} $$

A. $f^{-1}(x) = 7\sqrt{x}$

B. $f^{-1}(x) = \frac{1}{7x}$

C. $f^{-1}(x) = 7x$

D. $f^{-1}(x) = \frac{\sqrt{x}}{7}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Swap variables to find the inverse relation

Solve for y

Write in inverse function notation

Answer: